A wire of length L, are of cross section A is hanging from a fixed support. The length of the wire changed to L₁ when mass M is suspended from its free end. The expression for Young's modulus is :

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 $$ \times $$ 10^–2 N/m. The pressure inside the bubble equals at a point Z₀ below the free surface of water in a container. Taking g = 10 m/s², density of water = 10³ kg/m³, the value of Z₀ is :

A small hole of area of cross-section 2 mm² present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s², the rate of flow of water through the open hole would be nearly :

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + $$l$$). The elastic potential energy stored in the extended wire is :